A Zip file is just an archive. It stores other files. Sometimes software is distributed via zip files and contains an installer package. It sounds like you are describing software that is distributed in a ZIP file already "ready to go" without an installer. You would unzip the software where you want it and run it from there, or create the shortcuts you want. It is not something that requires any sort of specialized training, and I'm not sure where the idea that computers require specialized training to use comes from. They are designed to be easy to learn and utilize; It merely takes patience in becoming familiar with the aspects needed.
For example let's say you want to download a program called Revlar. What it does isn't important, because I just made it up. So the download link gives you REVLAR.ZIP. Alright.
Now as far as the contents go, there are a few possibilities once you unzip it- It may have an installer or setup program, which will install the software, or it might not.
The latter case seems to be the one to which you refer. In that instance typically the software will be an executable and perhaps some DLL files needed to run the program; perhaps REVLAR.EXE and REVLAR.DLL. The idea is you copy those files over to a location you want to install it. This is simply something you pick up with time as you become more familiar; you know certain file types are applications, and you see files that run alongside them in a ZIP file and it is pretty straightforward that it likely would need to be moved/installed to a folder via extracting it there.